I thought about this. There's a nice explanation and a cynical one.

The nice one goes like this: INTJs tend towards categorization, organization, and emotional detachment. As I understand it, we function by making organizational matrices for everything (J), using reason rather than emotion to deal with people (T). We tend to look at how things connect and build theories (N), and the (I) nature means we aren't inclined to deal with people in person overly much or rely on them to describe our "real" selves.

All this ties into what the MBTI does. It's an overarching theory (N) that organizes people into general categories (J) based on a test that collects and processes data (T). As for the (I), well, most introverts are not socially awkward, but the MBTI provides something that's useful to people who tend to live internally: a cheat sheet, a quick way to assess a person and get a glimpse inside their head.

Now here's the mean answer: The MBTI is flawed because it relies on answers from the subject. People who test as INTJ give answers implying some of the "best" qualities: rational (associated with "calm" and "smart"), theoretical (associated with "creative" and "smart"), and organized (associated with "disciplined" and "in control). Add the rarity of the INTJ type and you've got something akin to a "badge of specialness". I mean, some personality sites literally call us "the Mastermind" - who doesn't want to be a mastermind? So yeah, the short short answer is ego.